The present disclosure relates to a simulation method that simulates a shape of a workpiece in processing treatment, a simulation program and a simulator that execute the simulation method. The present disclosure also relates to processing equipment provided with the simulator and to a method of manufacturing a semiconductor device using the processing equipment.
There is process shape (etching, deposition) simulation as a technique to predict semiconductor processing, which is recognized by being roughly categorized in two models. One is a string model, and the other is a voxel model.
In the string model, grid points are arranged on the surface of the shape and a surface reaction is numerically solved at each grid point to derive a reaction rate, and further the coordinates of the grid points are moved in accordance with the reaction rate in the normal direction and each grid point is joined together by a string. The string model thus expresses development of the process shape.
In the string model, the normal line is derived using positional information of adjacent grid points, so that the derivation method is easy.
On the other hand, due to the characteristics of the derivation method, the string model is poor in capability to follow sharp change in shape and the strings sometimes turn out to cross each other.
In contrast, in the voxel model, a shape is expressed by determining whether or not an arranged voxel exists, so that the voxel model is good in reproducibility of a complex shape, such as a microtrench, compared with the string model.
Since the voxel model is generally a calculation approach using the Monte Carlo method, so that it is easy to simulate transfer of gas, such as ions or radicals in a pattern, and a micro physical phenomenon and a chemical reaction on the surface, and thus it is recognized as a useful approach to replace the string model.
As modeling of ion transfer in shape simulation using the voxel model, there are recognized mainly two methods.
One is a model based on the Monte Carlo method, and the other is a model based on the flux method.
With a model based on the Monte Carlo method, ions with energy distribution and incident angular distribution that are calculated in a sheath region, for example, are incident on a pattern to solve penetration, scattering, and propagation of ions to pattern side walls in the Monte Carlo method (for example, refer to Osano et al., Japanese Journal of Applied Physics, Vol. 45, No. 10B, (2006), pp. 8157-8162).
With a model based on the flux method, ion transfer is handled by solving a simultaneous reaction equation related to balance of an amount of an incident ion flux and an amount of reemission utilizing, for example, the radiosity method (for example, refer to Japanese Unexamined Patent Application Publication No. 2002-50553). That is, ion transfer is handled by solving an inverse matrix of iN×iN in a two-dimensional space and an inverse matrix of iN×iN×iN in a three-dimensional space (i denotes the number of particles contributing to the reaction, and N denotes the number of voxels existing on the surface). At this time, the scattering and the direct incidence are handled at the same time.